Help with piece-wise question very confusing

Question

Q: A tax bill is being considered that would tax the first $20,000 of an individual’s annual income at a rate of 15% and any income over $20,000 is taxed at 20%. 

 

a. Calculate the income tax for an individual earning $15,000 a year. Show your work.
my answer- $15,000*0.15=$2250

b. Calculate the income tax for an individual earning $45,000 a year. Show your work.
my answer- $20,000*0.15=$3000 and $25,000*0.2=$5000 which equals the $45,000

c. Derive piecewise-defined function to calculate the income tax T(E) in thousands of dollars as a function of the annual earning E in thousands of dollars (i.e “1” means $1000). Use appropriate piecewise notation to express the function as you learned in the activity for piecewise functions.

Answer 1

So in part (b), it is $8000 in taxes

 

 

T(E) =    0.15 * E if E<=20

 

              3 + (E-20)*0.2  if E>20

 

 where the domain is E>0

 

 

And yes, the graph on desmos.com does agree.

T(15) = 2.25 and T(45) = 8